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Central discontinuous Galerkin methods on overlapping meshes for wave equations

文献类型：期刊论文

作者Liu, Yong1; Lu, Jianfang2; Shu, Chi-Wang3; Zhang, Mengping4
刊名ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
出版日期2021-02-18
卷号55期号:1页码:329-356
关键词Optimal error estimates central DG method second order wave equation dispersion analysis
ISSN号0764-583X
DOI10.1051/m2an/2020069
英文摘要In this paper, we study the central discontinuous Galerkin (DG) method on overlapping meshes for second order wave equations. We consider the first order hyperbolic system, which is equivalent to the second order scalar equation, and construct the corresponding central DG scheme. We then provide the stability analysis and the optimal error estimates for the proposed central DG scheme for one- and multi-dimensional cases with piecewise P-k elements. The optimal error estimates are valid for uniform Cartesian meshes and polynomials of arbitrary degree k >= 0. In particular, we adopt the techniques in Liu et al. (SIAM J. Numer. Anal. 56 (2018) 520-541; ESAIM: M2AN 54 (2020) 705-726) and obtain the local projection that is crucial in deriving the optimal order of convergence. The construction of the projection here is more challenging since the unknowns are highly coupled in the proposed scheme. Dispersion analysis is performed on the proposed scheme for one dimensional problems, indicating that the numerical solution with P-1 elements reaches its minimum with a suitable parameter in the dissipation term. Several numerical examples including accuracy tests and long time simulation are presented to validate the theoretical results.
资助项目China Scholarship Council ; China Postdoctoral Science Foundation[2020TQ0343] ; NSFC[11871448] ; NSFC[11901213] ; NSF[DMS-1719410] ; NSF[DMS-2010107] ; AFOSR[FA9550-20-1-0055]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000619239500012
出版者EDP SCIENCES S A
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58185]  
专题中国科学院数学与系统科学研究院
通讯作者Lu, Jianfang
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Ctr Math Sci, Beijing 100190, Peoples R China
2.South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Guangdong, Peoples R China
3.Brown Univ, Div Appl Math, Providence, RI 02912 USA
4.Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
推荐引用方式
GB/T 7714		 Liu, Yong,Lu, Jianfang,Shu, Chi-Wang,et al. Central discontinuous Galerkin methods on overlapping meshes for wave equations[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,2021,55(1):329-356.
APA Liu, Yong,Lu, Jianfang,Shu, Chi-Wang,&Zhang, Mengping.(2021).Central discontinuous Galerkin methods on overlapping meshes for wave equations.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,55(1),329-356.
MLA Liu, Yong,et al."Central discontinuous Galerkin methods on overlapping meshes for wave equations".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 55.1(2021):329-356.

入库方式： OAI收割

来源：数学与系统科学研究院

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